Question

James is playing in a tennis competition. He is required to play 8 matches and he must win all 8 to win the competition.
He has 10 percent chance of winning the competition.
In each match his probability of winning decreases by 5 percent of the preceding match's probability.

What is the probability that he wins the first match?

Answer 1

15.513% ???

Answer 2

nope

Answer 3

14.07% ??

Answer 4

10% chances for winning competition.. i.e for winning all 8 matches..

say he has probability of winning in 1st match = x%

SO in every match , it reduces by 5%..

so probability for every match will be

x + (x-5) + (x-10) + (x-15 ) + (x -20) + (x-25) + (x-30) + (x-35) = 10
x + 7x -140 = 10
8x = 150
x= 150/8

x = 18.75 %

what say ??

Answer 5

doesnt look right..

Answer 6

it got to do somethig with gp's ..

Answer 7

reasoning as follows
put \(p\) as the probability he wins the first match, making the probability he wins the second match \(.95p\) and the third as \(.9p\) and so on
since winning 8 is an AND statement, you multiply these together and set it equal to .1
you would expect the probability he wins the first first to be rather large

Answer 8

looks like about .978 or around 98%

Answer 9

GP = ???
@satellite73 sir :)

Answer 10

i got it thanks.
and its 90.

Answer 11

really? i must have typed it in wrong

Answer 12

well this is how i did it..
\[(0.95)p * (0.95)^2p *....* (0.95)^7p = 0.1\]
then solved for p

Answer 13

oh yeah i did
it is about 92% right?

Answer 14

exactly 90

Answer 15

welll 0.89...

Answer 16

oh wow did i make a bush league mistake sorry

Answer 17

(blush)

Answer 18

why 0.95, 0.9, 0.85?

Answer 19

yes you have it
because i am an idiot, you are exactly right

Answer 20

what you have is correct, ignore me
now i better get some coffee